Skip to main content
SpringerLink
Log in

Point-in-Polygon Analysis Under Certainty and Uncertainty

  • Published:
GeoInformatica Aims and scope Submit manuscript

Abstract

The point-in-polygon query in geographical information systems under certainty and uncertainty is formally analyzed in this paper. It is argued that points and polygons can be precise, fuzzy (imprecise), and random (with error) with different schemes of representations. Under certainty, points and polygons can generally be represented by their characteristic functions. Under imprecision induced uncertainty, they can be represented by fuzzy sets characterized by membership functions. If uncertainty is induced by randomness, points and polygons can be described by locational error models in which probability arguments are employed. Points and polygons under certainty turn out to be a special case of that under imprecision and randomness induced uncertainty.

Since points and polygons may be precisely, imprecisely or randomly captured or recognized within a spatial information system, the point-in-polygon query is then rather complicated, and its entertainment is not straight forward. In general, the point-in-polygon query can be entertained under nine basic situations. It consists of the queries of whether a precise or fuzzy or random point is in a precise or fuzzy or random polygon. As a consequence, the answer to the query may take on various forms with certain types of uncertainty arguments attached. It involves the integrative utilization of fuzzy set and probability theories to derive the results.

The present analysis clarifies some unresolved issues of the point-in-polygon query and provides a generalization to its entertainment. Furthermore, it sheds light on the way certainty and uncertainty can be addressed and implemented in spatial information systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.F. Abler. “The National Science Foundation Center for Geographical Information and Analysis,” International Journal of Geographical Information Systems, 1:303–326, 1987.

    Google Scholar 

  2. D. Altman. “Fuzzy set theoretic approaches for handing imprecision in spatial analysis,” International Journal of Geographical Information Systems, 3:271–289, 1994.

    Google Scholar 

  3. M. Blakemore. “Generalization and error in spatial data bases,” Cartographica, 21:131–139, 1984.

    Google Scholar 

  4. P.V. Bolstad, P. Gessler, and T.M. Lillestand. “Positional uncertainty in manually digitized map data,” International Journal of Geographical Information Systems, 4:399–412, 1990.

    Google Scholar 

  5. F. Bouille. “Actual tools for cartography today,” Cartographica, 19:27–32, 1982.

    Google Scholar 

  6. P.A. Burrough, R.A. MacMillan, and W. Van Deursen. “Fuzzy classification methods to determine land suitability from soil profile observations and topography,” Journal of Soil Science, 43:120–193, 1992.

    Google Scholar 

  7. N.R. Chrisman. “A theory of cartographic error and its measurement in digital data bases,” Proceedings, Auto. Carto 5:159–168, 1982.

    Google Scholar 

  8. N.R. Chrisman. “The accuracy of map overlays: a reassessment,” Landscape and Urban Planning, 14:427–439, 1987.

    Google Scholar 

  9. N.R. Chrisman. “Modelling error in overlaid categorical maps,” in M.F. Goodchild, and S. Gopal (eds.), Accuracy of Spatial Databases, New York: Taylor and Francis, 21–34, 1989.

    Google Scholar 

  10. D. Dubois, and H. Prade. Possibility theory: an approach to computerized processing of uncertainty, New York: Plenum, 1988.

    Google Scholar 

  11. G. Edwards, and K.E. Lowell. “Modelling uncertainty in photointerpreted boundaries,” Photogrammetric Engineering & Remote Sensing, 62:377–391, 1996.

    Google Scholar 

  12. M.J. Egenhofer, and R.D. Franzosa. “Point-set topological spatial relations,” International Journal of Geographical Information Systems, 5:161–174, 1991.

    Google Scholar 

  13. W.R. Franklin. “Cartographic errors symptomatic of underlying algebra problems,” in Proceedings, International Symposium on Spatial Data Handling, University of Zurich, Zurich, 190–208, 1984.

    Google Scholar 

  14. W.R. Franklin, and P.Y.F. Wu. “A polygon overlay system in PROLOG,” in Proceedings, AutoCarto 8, ASPRS/ACSM, Falls Church, Virginia, 97–106, 1987.

    Google Scholar 

  15. M.F. Goodchild. “Modelling error in objects and fields,” in M.F. Goodchild, and S. Gopal (eds.), Accuracy of Spatial Databases, New York: Taylor and Francis, 107–114, 1989.

    Google Scholar 

  16. M.F. Goodchild. “Keynote address: symposium on spatial database accuracy,” in G.J. Hunter (ed.), Proceedings, Symposium on Spatial Database Accuracy, 1–16, 1991.

  17. M.F. Goodchild, and S. Gopal. (eds.) Accuracy of spatial databases, New York: Taylor and Francis, 1989.

    Google Scholar 

  18. G.B.M. Heuvelink, P. Burrough, and A. Stein. “Propagation of errors in spatial modelling with GIS,” International Journal of Geographical Information Systems, 3:303–322, 1989.

    Google Scholar 

  19. G.J. Hunter. (ed.) Proceedings of the Symposium on Spatial Database Accuracy, The University of Melbourne, Australia, 1991.

    Google Scholar 

  20. Y. Leung. Spatial analysis and planning under imprecision, Amsterdam: North-Holland, 1988.

    Google Scholar 

  21. Y. Leung. “Fuzzy logic and knowledge-based GIS: a prospectus,” in Proceedings, IGRASS'89 12th Canadian Symposium on Remote Sensing, 1:47–50, 1989.

    Google Scholar 

  22. Y. Leung, M.F. Goodchild, C.C. Lin. “Visualization of fuzzy scenes and probability fields,” in Proceedings, Fifth International Symposium on Spatial Data Handling, 2:480–490, 1992.

    Google Scholar 

  23. Y. Leung, and K.S. Leung. “An intelligent expert system shell for knowledge-based geographic information systems: 1, tools,” International Journal of Geographical Information Systems, 7:189–199, 1993a.

    Google Scholar 

  24. Y. Leung, and K.S. Leung. “An intelligent expert system shell for knowledge-based geographic information systems: 2, some applications,” International Journal of Geographical Information Systems, 7:201–213, 1993b.

    Google Scholar 

  25. Y. Leung, and J.P. Yan. “Locational error model for spatial features,” (unpublished paper), 1996.

  26. Y. Leung, J.S. Zhang, and Z.B. Xu. “Neural networks for convex hull computation,” IEEE Transactions on Neural Networks. (in press), 1997.

  27. K.E. Lowell. “Probabilistic temporal GIS modelling involving more than two map classes,” International Journal of Geographical Information Systems, 8:73–93, 1994.

    Google Scholar 

  28. D.H. Maling. “How long is a piece of string?,” The Cartographic Journal, 5:147–156, 1968.

    Google Scholar 

  29. J.C. Muller. “The concept of error in cartography,” Cartographica, 24:1–15, 1987.

    Google Scholar 

  30. J. Perkal. “On epsilon length,” Bulletin de l'Academie Polonaise des Sciences, 4:399–403, 1956.

    Google Scholar 

  31. F.P. Preparata, and M.I. Shamos. Computational geometry, an introduction, Berlin: Springer-Verlag, 1985.

    Google Scholar 

  32. M.L. Puri, and D.A. Ralescu. “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, 114:409–422, 1986.

    Google Scholar 

  33. H. Veregin. “Error modeling for the map overlay operation,” in M.F. Goodchild, and S. Gopal (eds.), Accuracy of Spatial Databases, New York: Taylor and Francis, Chapter 1, 1989a.

    Google Scholar 

  34. H. Veregin. Accuracy of spatial databases: annotated bibliography, Technical Report 89-9, Santa Barbara: National Center for Geographical Information and Analysis, University of California, 1989b.

    Google Scholar 

  35. H. Veregin. A taxonomy of error in spatial databases, Technical Report 89-12, Santa Barbara: National Center for Geographical Information and Analysis, University of California, 1989c.

    Google Scholar 

  36. H. Veregin. “Integration of simulation modeling and error propagation for the buffer operation in GIS,” Photogrammetric Engineering & Remote Sensing, 60:427–435, 1994.

    Google Scholar 

  37. H. Veregin. “Error propagation through the buffer operation for probability surfaces,” Photogrammetric Engineering & Remote Sensing, 62:419–428, 1996.

    Google Scholar 

  38. F. Wang. “Towards a natural language user interface: an approach of fuzzy query,” International Journal of Geographical Information Systems, 8:143–162, 1994.

    Google Scholar 

  39. R.R. Yager. “A note on probabilities of fuzzy events,” Information Sciences, 18:113–129, 1979.

    Google Scholar 

  40. L.A. Zadeh. “Probability measures of fuzzy events,” Journal of Mathematical Analysis and Applications, 23:421–427, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography and Centre for Environmental Studies, The Chinese University of Hong Kong, Shatin, Hong Kong

    YEE LEUNG

  2. Department of Resources and Environment, Beijing Normal University, Beijing, China

    JIANPING YAN

Authors
  1. YEE LEUNG
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JIANPING YAN
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

LEUNG, Y., YAN, J. Point-in-Polygon Analysis Under Certainty and Uncertainty. GeoInformatica 1, 93–114 (1997). https://doi.org/10.1023/A:1009764319102

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009764319102

Search

Navigation